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Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

If p and q are chosen randomly from the set 1,2,3,4,5,6,7,8,9,10 with replacement, then the probability that the roots of the equation x^2+p x+q=0

Options

  1. Aare real is 33 50
  2. Bare imaginary is 19 50
  3. Care real and equal is 3 100
  4. Dare real and distinct is 3 5

Correct answer

C. are real and equal is 3 100

Step-by-step solution

For real rools p^2 4 q Possible selections are as follows Probability for real roots = 62 100 = 31 50 For equal and real roots p^2=4 q aligned & (p, q)=(2,1),(4,4),(6,9) & Probability = 3 100 aligned Probability for imaginary roots =1- 3 50 = 19 50 Probability for real and distinct roots = 62 100 - 3 100 = 59 100 array ll p & q 1 & q 2 & 1 3 & 1.2 4 & 1,2,3,4 5 & 1,2, . .6 6 & 1 .9 7 & 1 .10 8 & 1 .10 9 & 1 10 10 & 1 10 Total =62 array

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